ALTERNATIVE IMPLEMENTATION

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_classification
%matplotlib inline

X, y = make_classification(n_samples=100000, n_features=2, n_redundant=0, n_repeated=0, 
                           n_informative=2, n_clusters_per_class=2, 
                           random_state=42) #for reproducibility 
fig, ax = plt.subplots() 
fig.set_size_inches(10, 10)
plt.scatter(X[:,0], X[:,1], marker='.')
plt.axis('off')
plt.show()
../_images/bebafcbf56a0c6c5748cb00ef741f35bb3d7ea39b779165f5fa133377c7c7dc2.png
from tqdm import tqdm

def dist(x,y):
    return np.linalg.norm(x-y)

def poprow(arr,i):
    pop = arr[i]
    new_array = np.vstack((arr[:i],arr[i+1:]))
    return new_array,pop

def cluster(X, p, k, dist_to_xr):
    c = [p]
    
    if dist_to_xr == None:
        distances = [dist(v,p) for v in X]
    else:
        distances = dist_to_xr
        
    X = X[np.argpartition(distances, k-1)]
    c.extend(X[:k-1])
    X = X[k-1:]
    
    return X, np.array(c)
    
def mdav(X, k):
    D = X
    clusters = []
    
    # Test feature. progress bar
    pbar = tqdm(total=len(D))
    
    while len(D) >= 3*k:
        # Centroid
        xm = np.mean(D, axis=0)
        # Furthest from centroid
        xri = np.argmax([dist(v,xm) for v in D])
        D, xr = poprow(D, xri)
        # Furthest from furthest from centroid
        dist_to_xr = [dist(v,xr) for v in D]
        xsi = np.argmax(dist_to_xr)
        dist_to_xr = dist_to_xr[:xsi]+dist_to_xr[xsi+1:]
        D, xs = poprow(D, xsi) 

        #cluster of xr
        D, c = cluster(D, xr, k, dist_to_xr)
        clusters.append(c)
        
        # Test feature. progress bar
        pbar.update(k)
        
        #cluster of xs
        D, c = cluster(D, xs, k, None)
        clusters.append(c)
        
        # Test feature. progress bar
        pbar.update(k)
        
    if len(D) >= 2*k and len(D) < 3*k:
        # Centroid
        xm = np.mean(D, axis=0)
        # Furthest from centroid
        xri = np.argmax([dist(v,xm) for v in D])
        D, xr = poprow(D, xri)
        #cluster of xr
        D, c = cluster(D, xr, k, None)
        clusters.append(c)
        
        # Test feature. progress bar
        pbar.update(k)
        
        # rest of points
        clusters.append(D[:]) 
        
        # Test feature. progress bar
        pbar.update(len(D))
        
    else:
        # rest of points
        clusters.append(D[:])
        
        # Test feature. progress bar
        pbar.update(len(D))
    
    centroids = np.array([np.mean(c,axis=0) for c in clusters], copy=False)
    
    return clusters, centroids

def print_stats(clusters, centroids):
    ss = []
    for c,cen in zip(clusters, centroids):
        #cen = np.mean(c, axis=0)
        s = np.mean([dist(x,cen) for x in c], axis=0)
        ss.append(s)
        
    print(f'Number of clusters: {len(clusters)}')
    print(f'Mean of mean distances to centroids: {np.mean(ss, axis=0)}')

def plot_results(clusters):
    fig, ax = plt.subplots() 
    fig.set_size_inches(10, 10)
    for c, cen in zip(clusters, centroids):
        plt.scatter(c[:,0], c[:,1], marker='.', s=25)
        #plt.scatter(cen[0], cen[1], marker='o', s=100, edgecolor='k')
    plt.axis('off')
    plt.show()
# Vanilla MDAV
k=5
clusters, centroids = mdav(X, k)
print_stats(clusters, centroids)
#plot_results(clusters)
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  1%|▋                                                                          | 975/100000 [02:08<4:06:02,  6.71it/s]
  1%|▋                                                                          | 980/100000 [02:08<3:38:56,  7.54it/s]
  1%|▋                                                                          | 985/100000 [02:09<4:06:14,  6.70it/s]
  1%|▋                                                                          | 990/100000 [02:09<3:38:15,  7.56it/s]
  1%|▋                                                                          | 995/100000 [02:10<4:05:16,  6.73it/s]
  1%|▋                                                                         | 1000/100000 [02:11<3:37:45,  7.58it/s]
  1%|▋                                                                         | 1005/100000 [02:12<4:05:39,  6.72it/s]
  1%|▋                                                                         | 1010/100000 [02:12<3:38:37,  7.55it/s]
  1%|▊                                                                         | 1015/100000 [02:13<4:05:52,  6.71it/s]
  1%|▊                                                                         | 1020/100000 [02:14<3:38:12,  7.56it/s]
  1%|▊                                                                         | 1025/100000 [02:15<4:05:54,  6.71it/s]
  1%|▊                                                                         | 1030/100000 [02:15<3:38:22,  7.55it/s]
  1%|▊                                                                         | 1035/100000 [02:16<4:05:12,  6.73it/s]
  1%|▊                                                                         | 1040/100000 [02:16<3:37:51,  7.57it/s]
  1%|▊                                                                         | 1045/100000 [02:17<4:06:55,  6.68it/s]
  1%|▊                                                                         | 1050/100000 [02:18<3:38:55,  7.53it/s]
  1%|▊                                                                         | 1055/100000 [02:19<4:08:40,  6.63it/s]
  1%|▊                                                                         | 1060/100000 [02:19<3:40:15,  7.49it/s]
  1%|▊                                                                         | 1065/100000 [02:20<4:07:57,  6.65it/s]
  1%|▊                                                                         | 1070/100000 [02:21<3:39:56,  7.50it/s]
  1%|▊                                                                         | 1075/100000 [02:22<4:06:21,  6.69it/s]
  1%|▊                                                                         | 1080/100000 [02:22<3:39:06,  7.52it/s]
  1%|▊                                                                         | 1085/100000 [02:23<4:05:53,  6.70it/s]
  1%|▊                                                                         | 1090/100000 [02:24<3:38:14,  7.55it/s]
  1%|▊                                                                         | 1095/100000 [02:25<4:05:25,  6.72it/s]
  1%|▊                                                                         | 1100/100000 [02:25<3:37:55,  7.56it/s]
  1%|▊                                                                         | 1105/100000 [02:26<4:04:31,  6.74it/s]
  1%|▊                                                                         | 1110/100000 [02:26<3:37:10,  7.59it/s]
  1%|▊                                                                         | 1115/100000 [02:27<4:03:49,  6.76it/s]
  1%|▊                                                                         | 1120/100000 [02:28<3:36:47,  7.60it/s]
  1%|▊                                                                         | 1125/100000 [02:29<4:04:00,  6.75it/s]
  1%|▊                                                                         | 1130/100000 [02:29<3:37:30,  7.58it/s]
  1%|▊                                                                         | 1135/100000 [02:30<4:04:31,  6.74it/s]
  1%|▊                                                                         | 1140/100000 [02:31<3:37:38,  7.57it/s]
  1%|▊                                                                         | 1145/100000 [02:32<4:05:15,  6.72it/s]
  1%|▊                                                                         | 1150/100000 [02:32<3:37:57,  7.56it/s]
  1%|▊                                                                         | 1155/100000 [02:33<4:06:53,  6.67it/s]
  1%|▊                                                                         | 1160/100000 [02:33<3:38:29,  7.54it/s]
  1%|▊                                                                         | 1165/100000 [02:34<4:05:08,  6.72it/s]
  1%|▊                                                                         | 1170/100000 [02:35<3:37:40,  7.57it/s]
  1%|▊                                                                         | 1175/100000 [02:36<4:05:30,  6.71it/s]
  1%|▊                                                                         | 1180/100000 [02:36<3:38:02,  7.55it/s]
  1%|▉                                                                         | 1185/100000 [02:37<4:05:29,  6.71it/s]
  1%|▉                                                                         | 1190/100000 [02:38<3:37:58,  7.56it/s]
  1%|▉                                                                         | 1195/100000 [02:39<4:04:00,  6.75it/s]
  1%|▉                                                                         | 1200/100000 [02:39<3:37:00,  7.59it/s]
  1%|▉                                                                         | 1205/100000 [02:40<4:04:19,  6.74it/s]
  1%|▉                                                                         | 1210/100000 [02:40<3:37:27,  7.57it/s]
  1%|▉                                                                         | 1215/100000 [02:41<4:04:35,  6.73it/s]
  1%|▉                                                                         | 1220/100000 [02:42<3:37:18,  7.58it/s]
  1%|▉                                                                         | 1225/100000 [02:43<4:04:30,  6.73it/s]
  1%|▉                                                                         | 1230/100000 [02:43<3:37:09,  7.58it/s]
  1%|▉                                                                         | 1235/100000 [02:44<4:05:05,  6.72it/s]
  1%|▉                                                                         | 1240/100000 [02:45<3:37:33,  7.57it/s]
  1%|▉                                                                         | 1245/100000 [02:46<4:04:45,  6.72it/s]
  1%|▉                                                                         | 1250/100000 [02:46<3:37:16,  7.57it/s]
  1%|▉                                                                         | 1255/100000 [02:47<4:04:03,  6.74it/s]
  1%|▉                                                                         | 1260/100000 [02:47<3:36:38,  7.60it/s]
  1%|▉                                                                         | 1265/100000 [02:48<4:02:56,  6.77it/s]
  1%|▉                                                                         | 1270/100000 [02:49<3:36:36,  7.60it/s]
  1%|▉                                                                         | 1275/100000 [02:50<4:03:21,  6.76it/s]
  1%|▉                                                                         | 1280/100000 [02:50<3:36:10,  7.61it/s]
  1%|▉                                                                         | 1285/100000 [02:51<4:02:56,  6.77it/s]
  1%|▉                                                                         | 1290/100000 [02:52<3:36:06,  7.61it/s]
  1%|▉                                                                         | 1295/100000 [02:53<4:02:58,  6.77it/s]
  1%|▉                                                                         | 1300/100000 [02:53<3:35:59,  7.62it/s]
  1%|▉                                                                         | 1305/100000 [02:54<4:03:27,  6.76it/s]
  1%|▉                                                                         | 1310/100000 [02:54<3:36:36,  7.59it/s]
  1%|▉                                                                         | 1315/100000 [02:55<4:03:09,  6.76it/s]
  1%|▉                                                                         | 1320/100000 [02:56<3:36:49,  7.59it/s]
  1%|▉                                                                         | 1325/100000 [02:57<4:03:19,  6.76it/s]
  1%|▉                                                                         | 1330/100000 [02:57<3:36:01,  7.61it/s]
  1%|▉                                                                         | 1335/100000 [02:58<4:03:34,  6.75it/s]
  1%|▉                                                                         | 1340/100000 [02:59<3:36:45,  7.59it/s]
  1%|▉                                                                         | 1345/100000 [03:00<4:03:14,  6.76it/s]
  1%|▉                                                                         | 1350/100000 [03:00<3:35:36,  7.63it/s]
  1%|█                                                                         | 1355/100000 [03:01<4:02:28,  6.78it/s]
  1%|█                                                                         | 1360/100000 [03:01<3:38:41,  7.52it/s]
  1%|█                                                                         | 1365/100000 [03:02<4:05:52,  6.69it/s]
  1%|█                                                                         | 1370/100000 [03:03<3:38:25,  7.53it/s]
  1%|█                                                                         | 1375/100000 [03:04<4:04:22,  6.73it/s]
  1%|█                                                                         | 1380/100000 [03:04<3:36:34,  7.59it/s]
  1%|█                                                                         | 1385/100000 [03:05<4:02:45,  6.77it/s]
  1%|█                                                                         | 1390/100000 [03:06<3:36:10,  7.60it/s]
  1%|█                                                                         | 1395/100000 [03:07<4:02:38,  6.77it/s]
  1%|█                                                                         | 1400/100000 [03:07<3:35:18,  7.63it/s]
  1%|█                                                                         | 1405/100000 [03:08<4:03:26,  6.75it/s]
  1%|█                                                                         | 1410/100000 [03:08<3:36:30,  7.59it/s]
  1%|█                                                                         | 1415/100000 [03:09<4:03:18,  6.75it/s]
  1%|█                                                                         | 1420/100000 [03:10<3:36:06,  7.60it/s]
  1%|█                                                                         | 1425/100000 [03:11<4:03:11,  6.76it/s]
  1%|█                                                                         | 1430/100000 [03:11<3:35:34,  7.62it/s]
  1%|█                                                                         | 1435/100000 [03:12<4:01:52,  6.79it/s]
  1%|█                                                                         | 1440/100000 [03:13<3:35:12,  7.63it/s]
  1%|█                                                                         | 1445/100000 [03:14<4:04:20,  6.72it/s]
  1%|█                                                                         | 1450/100000 [03:14<3:37:24,  7.56it/s]
  1%|█                                                                         | 1455/100000 [03:15<4:05:05,  6.70it/s]
  1%|█                                                                         | 1460/100000 [03:15<3:37:51,  7.54it/s]
  1%|█                                                                         | 1465/100000 [03:16<4:04:29,  6.72it/s]
  1%|█                                                                         | 1470/100000 [03:17<3:36:40,  7.58it/s]
  1%|█                                                                         | 1475/100000 [03:18<4:03:19,  6.75it/s]
  1%|█                                                                         | 1480/100000 [03:18<3:35:50,  7.61it/s]
  1%|█                                                                         | 1485/100000 [03:19<4:04:32,  6.71it/s]
  1%|█                                                                         | 1490/100000 [03:20<3:36:47,  7.57it/s]
  1%|█                                                                         | 1495/100000 [03:21<4:03:19,  6.75it/s]
  2%|█                                                                         | 1500/100000 [03:21<3:36:02,  7.60it/s]
  2%|█                                                                         | 1505/100000 [03:22<4:03:00,  6.76it/s]
  2%|█                                                                         | 1510/100000 [03:22<3:35:44,  7.61it/s]
  2%|█                                                                         | 1515/100000 [03:23<4:03:10,  6.75it/s]
  2%|█                                                                         | 1520/100000 [03:24<3:36:12,  7.59it/s]
  2%|█▏                                                                        | 1525/100000 [03:25<4:03:19,  6.75it/s]
  2%|█▏                                                                        | 1530/100000 [03:25<3:35:58,  7.60it/s]
  2%|█▏                                                                        | 1535/100000 [03:26<4:02:47,  6.76it/s]
  2%|█▏                                                                        | 1540/100000 [03:27<3:35:45,  7.61it/s]
  2%|█▏                                                                        | 1545/100000 [03:28<4:02:14,  6.77it/s]
  2%|█▏                                                                        | 1550/100000 [03:28<3:35:54,  7.60it/s]
  2%|█▏                                                                        | 1555/100000 [03:29<4:02:56,  6.75it/s]
  2%|█▏                                                                        | 1560/100000 [03:29<3:35:07,  7.63it/s]
  2%|█▏                                                                        | 1565/100000 [03:30<4:01:26,  6.79it/s]
  2%|█▏                                                                        | 1570/100000 [03:31<3:34:16,  7.66it/s]
  2%|█▏                                                                        | 1575/100000 [03:32<4:00:41,  6.82it/s]
  2%|█▏                                                                        | 1580/100000 [03:32<3:34:06,  7.66it/s]
  2%|█▏                                                                        | 1585/100000 [03:33<4:01:08,  6.80it/s]
  2%|█▏                                                                        | 1590/100000 [03:34<3:34:21,  7.65it/s]
  2%|█▏                                                                        | 1595/100000 [03:34<4:00:54,  6.81it/s]
  2%|█▏                                                                        | 1600/100000 [03:35<3:34:06,  7.66it/s]
  2%|█▏                                                                        | 1605/100000 [03:36<4:01:35,  6.79it/s]
  2%|█▏                                                                        | 1610/100000 [03:36<3:34:48,  7.63it/s]
  2%|█▏                                                                        | 1615/100000 [03:37<4:01:51,  6.78it/s]
  2%|█▏                                                                        | 1620/100000 [03:38<3:36:12,  7.58it/s]
  2%|█▏                                                                        | 1625/100000 [03:39<4:03:19,  6.74it/s]
  2%|█▏                                                                        | 1630/100000 [03:39<3:36:00,  7.59it/s]
  2%|█▏                                                                        | 1635/100000 [03:40<4:03:04,  6.74it/s]
  2%|█▏                                                                        | 1640/100000 [03:41<3:35:22,  7.61it/s]
  2%|█▏                                                                        | 1645/100000 [03:41<4:01:50,  6.78it/s]
  2%|█▏                                                                        | 1650/100000 [03:42<3:34:42,  7.63it/s]
  2%|█▏                                                                        | 1655/100000 [03:43<4:01:49,  6.78it/s]
  2%|█▏                                                                        | 1660/100000 [03:43<3:37:55,  7.52it/s]
  2%|█▏                                                                        | 1665/100000 [03:44<4:03:17,  6.74it/s]
  2%|█▏                                                                        | 1670/100000 [03:45<3:35:49,  7.59it/s]
  2%|█▏                                                                        | 1675/100000 [03:46<4:02:21,  6.76it/s]
  2%|█▏                                                                        | 1680/100000 [03:46<3:35:03,  7.62it/s]
  2%|█▏                                                                        | 1685/100000 [03:47<4:01:42,  6.78it/s]
  2%|█▎                                                                        | 1690/100000 [03:48<3:35:09,  7.62it/s]
  2%|█▎                                                                        | 1695/100000 [03:48<4:01:44,  6.78it/s]
  2%|█▎                                                                        | 1700/100000 [03:49<3:34:50,  7.63it/s]
  2%|█▎                                                                        | 1705/100000 [03:50<4:01:37,  6.78it/s]
  2%|█▎                                                                        | 1710/100000 [03:50<3:34:35,  7.63it/s]
  2%|█▎                                                                        | 1715/100000 [03:51<4:02:03,  6.77it/s]
  2%|█▎                                                                        | 1720/100000 [03:52<3:34:59,  7.62it/s]
  2%|█▎                                                                        | 1725/100000 [03:53<4:02:31,  6.75it/s]
  2%|█▎                                                                        | 1730/100000 [03:53<3:35:06,  7.61it/s]
  2%|█▎                                                                        | 1735/100000 [03:54<4:02:33,  6.75it/s]
  2%|█▎                                                                        | 1740/100000 [03:54<3:34:59,  7.62it/s]
  2%|█▎                                                                        | 1745/100000 [03:55<4:02:10,  6.76it/s]
  2%|█▎                                                                        | 1750/100000 [03:56<3:34:46,  7.62it/s]
  2%|█▎                                                                        | 1755/100000 [03:57<4:01:03,  6.79it/s]
  2%|█▎                                                                        | 1760/100000 [03:57<3:34:44,  7.62it/s]
  2%|█▎                                                                        | 1765/100000 [03:58<4:00:53,  6.80it/s]
  2%|█▎                                                                        | 1770/100000 [03:59<3:34:08,  7.65it/s]
  2%|█▎                                                                        | 1775/100000 [04:00<4:00:39,  6.80it/s]
  2%|█▎                                                                        | 1780/100000 [04:00<3:34:05,  7.65it/s]
  2%|█▎                                                                        | 1785/100000 [04:01<4:01:11,  6.79it/s]
  2%|█▎                                                                        | 1790/100000 [04:01<3:34:13,  7.64it/s]
  2%|█▎                                                                        | 1795/100000 [04:02<4:00:31,  6.81it/s]
  2%|█▎                                                                        | 1800/100000 [04:03<3:33:30,  7.67it/s]
  2%|█▎                                                                        | 1805/100000 [04:04<4:00:27,  6.81it/s]
  2%|█▎                                                                        | 1810/100000 [04:04<3:34:08,  7.64it/s]
  2%|█▎                                                                        | 1815/100000 [04:05<4:01:18,  6.78it/s]
  2%|█▎                                                                        | 1820/100000 [04:06<3:33:55,  7.65it/s]
  2%|█▎                                                                        | 1825/100000 [04:07<4:01:09,  6.79it/s]
  2%|█▎                                                                        | 1830/100000 [04:07<3:34:19,  7.63it/s]
  2%|█▎                                                                        | 1835/100000 [04:08<4:00:54,  6.79it/s]
  2%|█▎                                                                        | 1840/100000 [04:08<3:34:31,  7.63it/s]
  2%|█▎                                                                        | 1845/100000 [04:09<4:00:45,  6.79it/s]
  2%|█▎                                                                        | 1850/100000 [04:10<3:34:32,  7.63it/s]
  2%|█▎                                                                        | 1855/100000 [04:11<4:01:01,  6.79it/s]
  2%|█▍                                                                        | 1860/100000 [04:11<3:34:04,  7.64it/s]
  2%|█▍                                                                        | 1865/100000 [04:12<4:00:29,  6.80it/s]
  2%|█▍                                                                        | 1870/100000 [04:13<3:34:08,  7.64it/s]
  2%|█▍                                                                        | 1875/100000 [04:13<4:00:41,  6.79it/s]
  2%|█▍                                                                        | 1880/100000 [04:14<3:34:08,  7.64it/s]
  2%|█▍                                                                        | 1885/100000 [04:15<4:00:48,  6.79it/s]
  2%|█▍                                                                        | 1890/100000 [04:15<3:33:27,  7.66it/s]
  2%|█▍                                                                        | 1895/100000 [04:16<4:00:25,  6.80it/s]
  2%|█▍                                                                        | 1900/100000 [04:17<3:33:53,  7.64it/s]
  2%|█▍                                                                        | 1905/100000 [04:18<4:01:05,  6.78it/s]
  2%|█▍                                                                        | 1910/100000 [04:18<3:33:49,  7.65it/s]
  2%|█▍                                                                        | 1915/100000 [04:19<4:00:57,  6.78it/s]
  2%|█▍                                                                        | 1920/100000 [04:20<3:33:35,  7.65it/s]
  2%|█▍                                                                        | 1925/100000 [04:20<4:01:21,  6.77it/s]
  2%|█▍                                                                        | 1930/100000 [04:21<3:34:24,  7.62it/s]
  2%|█▍                                                                        | 1935/100000 [04:22<4:01:53,  6.76it/s]
  2%|█▍                                                                        | 1940/100000 [04:22<3:34:57,  7.60it/s]
  2%|█▍                                                                        | 1945/100000 [04:23<4:05:32,  6.66it/s]
  2%|█▍                                                                        | 1950/100000 [04:24<3:37:34,  7.51it/s]
  2%|█▍                                                                        | 1955/100000 [04:25<4:03:07,  6.72it/s]
  2%|█▍                                                                        | 1960/100000 [04:25<3:35:24,  7.59it/s]
  2%|█▍                                                                        | 1965/100000 [04:26<4:02:00,  6.75it/s]
  2%|█▍                                                                        | 1970/100000 [04:27<3:34:37,  7.61it/s]
  2%|█▍                                                                        | 1975/100000 [04:27<4:02:03,  6.75it/s]
  2%|█▍                                                                        | 1980/100000 [04:28<3:35:19,  7.59it/s]
  2%|█▍                                                                        | 1985/100000 [04:29<4:03:35,  6.71it/s]
  2%|█▍                                                                        | 1990/100000 [04:29<3:36:23,  7.55it/s]
  2%|█▍                                                                        | 1995/100000 [04:30<4:03:18,  6.71it/s]
  2%|█▍                                                                        | 2000/100000 [04:31<3:35:35,  7.58it/s]
  2%|█▍                                                                        | 2005/100000 [04:32<4:02:08,  6.74it/s]
  2%|█▍                                                                        | 2010/100000 [04:32<3:35:09,  7.59it/s]
  2%|█▍                                                                        | 2015/100000 [04:33<4:00:17,  6.80it/s]
  2%|█▍                                                                        | 2020/100000 [04:34<3:33:57,  7.63it/s]
  2%|█▍                                                                        | 2025/100000 [04:34<4:00:18,  6.79it/s]
  2%|█▌                                                                        | 2030/100000 [04:35<3:33:18,  7.66it/s]
  2%|█▌                                                                        | 2035/100000 [04:36<3:59:55,  6.81it/s]
  2%|█▌                                                                        | 2040/100000 [04:36<3:33:21,  7.65it/s]
  2%|█▌                                                                        | 2045/100000 [04:37<3:59:25,  6.82it/s]
  2%|█▌                                                                        | 2050/100000 [04:38<3:32:54,  7.67it/s]
  2%|█▌                                                                        | 2055/100000 [04:39<4:00:23,  6.79it/s]
  2%|█▌                                                                        | 2060/100000 [04:39<3:34:22,  7.61it/s]
  2%|█▌                                                                        | 2065/100000 [04:40<4:00:56,  6.77it/s]
  2%|█▌                                                                        | 2070/100000 [04:40<3:34:04,  7.62it/s]
  2%|█▌                                                                        | 2075/100000 [04:41<4:02:29,  6.73it/s]
  2%|█▌                                                                        | 2080/100000 [04:42<3:35:12,  7.58it/s]
  2%|█▌                                                                        | 2085/100000 [04:43<4:02:01,  6.74it/s]
  2%|█▌                                                                        | 2090/100000 [04:43<3:34:29,  7.61it/s]
  2%|█▌                                                                        | 2095/100000 [04:44<3:59:54,  6.80it/s]
  2%|█▌                                                                        | 2100/100000 [04:45<3:32:36,  7.67it/s]
  2%|█▌                                                                        | 2105/100000 [04:46<4:50:19,  5.62it/s]
  2%|█▌                                                                        | 2110/100000 [04:47<4:12:02,  6.47it/s]
  2%|█▌                                                                        | 2115/100000 [04:48<4:26:49,  6.11it/s]
  2%|█▌                                                                        | 2120/100000 [04:48<3:51:42,  7.04it/s]
  2%|█▌                                                                        | 2125/100000 [04:49<4:14:12,  6.42it/s]
  2%|█▌                                                                        | 2130/100000 [04:49<3:43:46,  7.29it/s]
  2%|█▌                                                                        | 2135/100000 [04:50<4:06:49,  6.61it/s]
  2%|█▌                                                                        | 2140/100000 [04:51<3:38:10,  7.48it/s]
  2%|█▌                                                                        | 2145/100000 [04:52<4:04:16,  6.68it/s]
  2%|█▌                                                                        | 2150/100000 [04:52<3:37:58,  7.48it/s]
  2%|█▌                                                                        | 2155/100000 [04:53<4:04:37,  6.67it/s]
  2%|█▌                                                                        | 2160/100000 [04:54<3:37:03,  7.51it/s]
  2%|█▌                                                                        | 2165/100000 [04:55<4:02:42,  6.72it/s]
  2%|█▌                                                                        | 2170/100000 [04:55<3:35:17,  7.57it/s]
  2%|█▌                                                                        | 2175/100000 [04:56<4:02:11,  6.73it/s]
  2%|█▌                                                                        | 2180/100000 [04:56<3:34:04,  7.62it/s]
  2%|█▌                                                                        | 2185/100000 [04:57<3:59:13,  6.81it/s]
  2%|█▌                                                                        | 2190/100000 [04:58<3:32:04,  7.69it/s]
  2%|█▌                                                                        | 2195/100000 [04:59<4:00:01,  6.79it/s]
  2%|█▋                                                                        | 2200/100000 [04:59<3:32:41,  7.66it/s]
  2%|█▋                                                                        | 2205/100000 [05:00<3:59:34,  6.80it/s]
  2%|█▋                                                                        | 2210/100000 [05:01<3:32:19,  7.68it/s]
  2%|█▋                                                                        | 2215/100000 [05:01<3:58:49,  6.82it/s]
  2%|█▋                                                                        | 2220/100000 [05:02<3:31:43,  7.70it/s]
  2%|█▋                                                                        | 2225/100000 [05:03<3:57:29,  6.86it/s]
  2%|█▋                                                                        | 2230/100000 [05:03<3:30:46,  7.73it/s]
  2%|█▋                                                                        | 2235/100000 [05:04<3:57:24,  6.86it/s]
  2%|█▋                                                                        | 2240/100000 [05:05<3:30:56,  7.72it/s]
  2%|█▋                                                                        | 2245/100000 [05:06<3:58:52,  6.82it/s]
  2%|█▋                                                                        | 2250/100000 [05:06<3:31:48,  7.69it/s]
  2%|█▋                                                                        | 2255/100000 [05:07<4:01:37,  6.74it/s]
  2%|█▋                                                                        | 2260/100000 [05:07<3:34:16,  7.60it/s]
  2%|█▋                                                                        | 2265/100000 [05:08<4:00:22,  6.78it/s]
  2%|█▋                                                                        | 2270/100000 [05:09<3:33:21,  7.63it/s]
  2%|█▋                                                                        | 2275/100000 [05:10<3:58:54,  6.82it/s]
  2%|█▋                                                                        | 2280/100000 [05:10<3:32:22,  7.67it/s]
  2%|█▋                                                                        | 2285/100000 [05:11<3:58:36,  6.83it/s]
  2%|█▋                                                                        | 2290/100000 [05:12<3:31:56,  7.68it/s]
  2%|█▋                                                                        | 2295/100000 [05:13<3:59:15,  6.81it/s]
  2%|█▋                                                                        | 2300/100000 [05:13<3:32:14,  7.67it/s]
  2%|█▋                                                                        | 2305/100000 [05:14<3:59:00,  6.81it/s]
  2%|█▋                                                                        | 2310/100000 [05:14<3:31:37,  7.69it/s]
  2%|█▋                                                                        | 2315/100000 [05:15<3:57:45,  6.85it/s]
  2%|█▋                                                                        | 2320/100000 [05:16<3:31:42,  7.69it/s]
  2%|█▋                                                                        | 2325/100000 [05:17<3:58:39,  6.82it/s]
  2%|█▋                                                                        | 2330/100000 [05:17<3:32:03,  7.68it/s]
  2%|█▋                                                                        | 2335/100000 [05:18<3:58:43,  6.82it/s]
  2%|█▋                                                                        | 2340/100000 [05:19<3:31:33,  7.69it/s]
  2%|█▋                                                                        | 2345/100000 [05:19<3:57:29,  6.85it/s]
  2%|█▋                                                                        | 2350/100000 [05:20<3:30:46,  7.72it/s]
  2%|█▋                                                                        | 2355/100000 [05:21<3:58:33,  6.82it/s]
  2%|█▋                                                                        | 2360/100000 [05:21<3:31:50,  7.68it/s]
  2%|█▊                                                                        | 2365/100000 [05:22<3:57:54,  6.84it/s]
  2%|█▊                                                                        | 2370/100000 [05:23<3:31:14,  7.70it/s]
  2%|█▊                                                                        | 2375/100000 [05:24<3:56:48,  6.87it/s]
  2%|█▊                                                                        | 2380/100000 [05:24<3:30:20,  7.74it/s]
  2%|█▊                                                                        | 2385/100000 [05:25<3:56:59,  6.86it/s]
  2%|█▊                                                                        | 2390/100000 [05:25<3:30:02,  7.75it/s]
  2%|█▊                                                                        | 2395/100000 [05:26<3:55:53,  6.90it/s]
  2%|█▊                                                                        | 2400/100000 [05:27<3:29:44,  7.76it/s]
  2%|█▊                                                                        | 2405/100000 [05:28<3:55:22,  6.91it/s]
  2%|█▊                                                                        | 2410/100000 [05:28<3:29:07,  7.78it/s]
  2%|█▊                                                                        | 2415/100000 [05:29<3:55:53,  6.89it/s]
  2%|█▊                                                                        | 2420/100000 [05:30<3:29:35,  7.76it/s]
  2%|█▊                                                                        | 2425/100000 [05:30<3:56:11,  6.89it/s]
  2%|█▊                                                                        | 2430/100000 [05:31<3:29:49,  7.75it/s]
  2%|█▊                                                                        | 2435/100000 [05:32<3:57:06,  6.86it/s]
  2%|█▊                                                                        | 2440/100000 [05:32<3:30:47,  7.71it/s]
  2%|█▊                                                                        | 2445/100000 [05:33<3:56:38,  6.87it/s]
  2%|█▊                                                                        | 2450/100000 [05:34<3:30:42,  7.72it/s]
  2%|█▊                                                                        | 2455/100000 [05:35<3:56:47,  6.87it/s]
  2%|█▊                                                                        | 2460/100000 [05:35<3:30:23,  7.73it/s]
  2%|█▊                                                                        | 2465/100000 [05:36<3:56:40,  6.87it/s]
  2%|█▊                                                                        | 2470/100000 [05:36<3:30:18,  7.73it/s]
  2%|█▊                                                                        | 2475/100000 [05:37<3:57:09,  6.85it/s]
  2%|█▊                                                                        | 2480/100000 [05:38<3:30:36,  7.72it/s]
  2%|█▊                                                                        | 2485/100000 [05:39<3:55:38,  6.90it/s]
  2%|█▊                                                                        | 2490/100000 [05:39<3:29:24,  7.76it/s]
  2%|█▊                                                                        | 2495/100000 [05:40<3:56:10,  6.88it/s]
  2%|█▊                                                                        | 2500/100000 [05:41<3:29:50,  7.74it/s]
  3%|█▊                                                                        | 2505/100000 [05:41<3:55:41,  6.89it/s]
  3%|█▊                                                                        | 2510/100000 [05:42<3:29:45,  7.75it/s]
  3%|█▊                                                                        | 2515/100000 [05:43<3:57:05,  6.85it/s]
  3%|█▊                                                                        | 2520/100000 [05:43<3:30:29,  7.72it/s]
  3%|█▊                                                                        | 2525/100000 [05:44<3:56:05,  6.88it/s]
  3%|█▊                                                                        | 2530/100000 [05:45<3:30:07,  7.73it/s]
  3%|█▉                                                                        | 2535/100000 [05:46<3:56:12,  6.88it/s]
  3%|█▉                                                                        | 2540/100000 [05:46<3:29:51,  7.74it/s]
  3%|█▉                                                                        | 2545/100000 [05:47<3:59:15,  6.79it/s]
  3%|█▉                                                                        | 2550/100000 [05:47<3:31:33,  7.68it/s]
  3%|█▉                                                                        | 2555/100000 [05:48<3:57:17,  6.84it/s]
  3%|█▉                                                                        | 2560/100000 [05:49<3:30:32,  7.71it/s]
  3%|█▉                                                                        | 2565/100000 [05:50<3:55:49,  6.89it/s]
  3%|█▉                                                                        | 2570/100000 [05:50<3:29:13,  7.76it/s]
  3%|█▉                                                                        | 2575/100000 [05:51<3:55:44,  6.89it/s]
  3%|█▉                                                                        | 2580/100000 [05:52<3:29:17,  7.76it/s]
  3%|█▉                                                                        | 2585/100000 [05:52<3:54:44,  6.92it/s]
  3%|█▉                                                                        | 2590/100000 [05:53<3:28:45,  7.78it/s]
  3%|█▉                                                                        | 2595/100000 [05:54<3:55:27,  6.89it/s]
  3%|█▉                                                                        | 2600/100000 [05:54<3:29:23,  7.75it/s]
  3%|█▉                                                                        | 2605/100000 [05:55<3:55:44,  6.89it/s]
  3%|█▉                                                                        | 2610/100000 [05:56<3:29:02,  7.76it/s]
  3%|█▉                                                                        | 2615/100000 [05:57<3:56:36,  6.86it/s]
  3%|█▉                                                                        | 2620/100000 [05:57<3:29:58,  7.73it/s]
  3%|█▉                                                                        | 2625/100000 [05:58<3:56:07,  6.87it/s]
  3%|█▉                                                                        | 2630/100000 [05:58<3:29:41,  7.74it/s]
  3%|█▉                                                                        | 2635/100000 [05:59<3:56:14,  6.87it/s]
  3%|█▉                                                                        | 2640/100000 [06:00<3:29:46,  7.74it/s]
  3%|█▉                                                                        | 2645/100000 [06:01<3:57:07,  6.84it/s]
  3%|█▉                                                                        | 2650/100000 [06:01<3:30:09,  7.72it/s]
  3%|█▉                                                                        | 2655/100000 [06:02<3:56:06,  6.87it/s]
  3%|█▉                                                                        | 2660/100000 [06:02<3:29:31,  7.74it/s]
  3%|█▉                                                                        | 2665/100000 [06:03<3:55:49,  6.88it/s]
  3%|█▉                                                                        | 2670/100000 [06:04<3:29:29,  7.74it/s]
  3%|█▉                                                                        | 2675/100000 [06:05<3:56:16,  6.87it/s]
  3%|█▉                                                                        | 2680/100000 [06:05<3:29:51,  7.73it/s]
  3%|█▉                                                                        | 2685/100000 [06:06<3:55:37,  6.88it/s]
  3%|█▉                                                                        | 2690/100000 [06:07<3:29:40,  7.74it/s]
  3%|█▉                                                                        | 2695/100000 [06:08<3:55:41,  6.88it/s]
  3%|█▉                                                                        | 2700/100000 [06:08<3:29:15,  7.75it/s]
  3%|██                                                                        | 2705/100000 [06:09<3:55:32,  6.88it/s]
  3%|██                                                                        | 2710/100000 [06:09<3:29:11,  7.75it/s]
  3%|██                                                                        | 2715/100000 [06:10<3:56:35,  6.85it/s]
  3%|██                                                                        | 2720/100000 [06:11<3:29:55,  7.72it/s]
  3%|██                                                                        | 2725/100000 [06:12<3:56:00,  6.87it/s]
  3%|██                                                                        | 2730/100000 [06:12<3:29:50,  7.73it/s]
  3%|██                                                                        | 2735/100000 [06:13<3:56:19,  6.86it/s]
  3%|██                                                                        | 2740/100000 [06:13<3:29:37,  7.73it/s]
  3%|██                                                                        | 2745/100000 [06:14<3:56:45,  6.85it/s]
  3%|██                                                                        | 2750/100000 [06:15<3:30:13,  7.71it/s]
  3%|██                                                                        | 2755/100000 [06:16<3:56:36,  6.85it/s]
  3%|██                                                                        | 2760/100000 [06:16<3:29:28,  7.74it/s]
  3%|██                                                                        | 2765/100000 [06:17<3:56:10,  6.86it/s]
  3%|██                                                                        | 2770/100000 [06:18<3:29:22,  7.74it/s]
  3%|██                                                                        | 2775/100000 [06:19<3:59:53,  6.75it/s]
  3%|██                                                                        | 2780/100000 [06:19<3:33:32,  7.59it/s]
  3%|██                                                                        | 2785/100000 [06:20<4:00:42,  6.73it/s]
  3%|██                                                                        | 2790/100000 [06:20<3:33:08,  7.60it/s]
  3%|██                                                                        | 2795/100000 [06:21<3:58:08,  6.80it/s]
  3%|██                                                                        | 2800/100000 [06:22<3:31:16,  7.67it/s]
  3%|██                                                                        | 2805/100000 [06:23<3:58:03,  6.80it/s]
  3%|██                                                                        | 2810/100000 [06:23<3:30:38,  7.69it/s]
  3%|██                                                                        | 2815/100000 [06:24<3:57:41,  6.81it/s]
  3%|██                                                                        | 2820/100000 [06:25<3:31:18,  7.66it/s]
  3%|██                                                                        | 2825/100000 [06:25<3:56:52,  6.84it/s]
  3%|██                                                                        | 2830/100000 [06:26<3:30:34,  7.69it/s]
  3%|██                                                                        | 2835/100000 [06:27<4:00:36,  6.73it/s]
  3%|██                                                                        | 2840/100000 [06:27<3:32:41,  7.61it/s]
  3%|██                                                                        | 2845/100000 [06:28<3:58:35,  6.79it/s]
  3%|██                                                                        | 2850/100000 [06:29<3:31:42,  7.65it/s]
  3%|██                                                                        | 2855/100000 [06:30<3:58:55,  6.78it/s]
  3%|██                                                                        | 2860/100000 [06:30<3:31:50,  7.64it/s]
  3%|██                                                                        | 2865/100000 [06:31<3:58:33,  6.79it/s]
  3%|██                                                                        | 2870/100000 [06:32<3:32:17,  7.63it/s]
  3%|██▏                                                                       | 2875/100000 [06:32<3:57:53,  6.80it/s]
  3%|██▏                                                                       | 2880/100000 [06:33<3:30:47,  7.68it/s]
  3%|██▏                                                                       | 2885/100000 [06:34<3:56:20,  6.85it/s]
  3%|██▏                                                                       | 2890/100000 [06:34<3:30:19,  7.70it/s]
  3%|██▏                                                                       | 2895/100000 [06:35<3:57:10,  6.82it/s]
  3%|██▏                                                                       | 2900/100000 [06:36<3:30:52,  7.67it/s]
  3%|██▏                                                                       | 2905/100000 [06:37<3:57:02,  6.83it/s]
  3%|██▏                                                                       | 2910/100000 [06:37<3:30:22,  7.69it/s]
  3%|██▏                                                                       | 2915/100000 [06:38<3:57:01,  6.83it/s]
  3%|██▏                                                                       | 2920/100000 [06:38<3:29:56,  7.71it/s]
  3%|██▏                                                                       | 2925/100000 [06:39<3:56:48,  6.83it/s]
  3%|██▏                                                                       | 2930/100000 [06:40<3:31:03,  7.67it/s]
  3%|██▏                                                                       | 2935/100000 [06:41<3:56:09,  6.85it/s]
  3%|██▏                                                                       | 2940/100000 [06:41<3:30:20,  7.69it/s]
  3%|██▏                                                                       | 2945/100000 [06:42<3:56:53,  6.83it/s]
  3%|██▏                                                                       | 2950/100000 [06:43<3:31:28,  7.65it/s]
  3%|██▏                                                                       | 2955/100000 [06:44<3:56:32,  6.84it/s]
  3%|██▏                                                                       | 2960/100000 [06:44<3:29:51,  7.71it/s]
  3%|██▏                                                                       | 2965/100000 [06:45<3:56:00,  6.85it/s]
  3%|██▏                                                                       | 2970/100000 [06:45<3:29:03,  7.74it/s]
  3%|██▏                                                                       | 2975/100000 [06:46<3:54:26,  6.90it/s]
  3%|██▏                                                                       | 2980/100000 [06:47<3:28:33,  7.75it/s]
  3%|██▏                                                                       | 2985/100000 [06:48<3:55:01,  6.88it/s]
  3%|██▏                                                                       | 2990/100000 [06:48<3:28:21,  7.76it/s]
  3%|██▏                                                                       | 2995/100000 [06:49<3:53:58,  6.91it/s]
  3%|██▏                                                                       | 3000/100000 [06:49<3:27:59,  7.77it/s]
  3%|██▏                                                                       | 3005/100000 [06:50<3:54:19,  6.90it/s]
  3%|██▏                                                                       | 3010/100000 [06:51<3:27:57,  7.77it/s]
  3%|██▏                                                                       | 3015/100000 [06:52<3:53:35,  6.92it/s]
  3%|██▏                                                                       | 3020/100000 [06:52<3:27:36,  7.79it/s]
  3%|██▏                                                                       | 3025/100000 [06:53<3:53:19,  6.93it/s]
  3%|██▏                                                                       | 3030/100000 [06:54<3:27:41,  7.78it/s]
  3%|██▏                                                                       | 3035/100000 [06:54<3:54:04,  6.90it/s]
  3%|██▏                                                                       | 3040/100000 [06:55<3:27:59,  7.77it/s]
  3%|██▎                                                                       | 3045/100000 [06:56<3:56:17,  6.84it/s]
  3%|██▎                                                                       | 3050/100000 [06:56<3:29:03,  7.73it/s]
  3%|██▎                                                                       | 3055/100000 [06:57<3:54:33,  6.89it/s]
  3%|██▎                                                                       | 3060/100000 [06:58<3:27:52,  7.77it/s]
  3%|██▎                                                                       | 3065/100000 [06:59<3:52:56,  6.94it/s]
  3%|██▎                                                                       | 3070/100000 [06:59<3:27:19,  7.79it/s]
  3%|██▎                                                                       | 3075/100000 [07:00<3:52:51,  6.94it/s]
  3%|██▎                                                                       | 3080/100000 [07:00<3:26:54,  7.81it/s]
  3%|██▎                                                                       | 3085/100000 [07:01<3:53:22,  6.92it/s]
  3%|██▎                                                                       | 3090/100000 [07:02<3:27:26,  7.79it/s]
  3%|██▎                                                                       | 3095/100000 [07:03<3:53:18,  6.92it/s]
  3%|██▎                                                                       | 3100/100000 [07:03<3:27:04,  7.80it/s]
  3%|██▎                                                                       | 3105/100000 [07:04<3:54:26,  6.89it/s]
  3%|██▎                                                                       | 3110/100000 [07:04<3:27:58,  7.76it/s]
  3%|██▎                                                                       | 3115/100000 [07:05<3:53:44,  6.91it/s]
  3%|██▎                                                                       | 3120/100000 [07:06<3:27:46,  7.77it/s]
  3%|██▎                                                                       | 3125/100000 [07:07<3:54:15,  6.89it/s]
  3%|██▎                                                                       | 3130/100000 [07:07<3:27:42,  7.77it/s]
  3%|██▎                                                                       | 3135/100000 [07:08<3:54:05,  6.90it/s]
  3%|██▎                                                                       | 3140/100000 [07:09<3:28:41,  7.74it/s]
  3%|██▎                                                                       | 3145/100000 [07:10<3:57:40,  6.79it/s]
  3%|██▎                                                                       | 3150/100000 [07:10<3:30:24,  7.67it/s]
  3%|██▎                                                                       | 3155/100000 [07:11<3:54:52,  6.87it/s]
  3%|██▎                                                                       | 3160/100000 [07:11<3:28:28,  7.74it/s]
  3%|██▎                                                                       | 3165/100000 [07:12<3:54:58,  6.87it/s]
  3%|██▎                                                                       | 3170/100000 [07:13<3:28:00,  7.76it/s]
  3%|██▎                                                                       | 3175/100000 [07:14<3:54:53,  6.87it/s]
  3%|██▎                                                                       | 3180/100000 [07:14<3:28:57,  7.72it/s]
  3%|██▎                                                                       | 3185/100000 [07:15<3:55:51,  6.84it/s]
  3%|██▎                                                                       | 3190/100000 [07:15<3:29:28,  7.70it/s]
  3%|██▎                                                                       | 3195/100000 [07:16<3:54:28,  6.88it/s]
  3%|██▎                                                                       | 3200/100000 [07:17<3:28:06,  7.75it/s]
  3%|██▎                                                                       | 3205/100000 [07:18<3:54:22,  6.88it/s]
  3%|██▍                                                                       | 3210/100000 [07:18<3:28:02,  7.75it/s]
  3%|██▍                                                                       | 3215/100000 [07:19<3:53:28,  6.91it/s]
  3%|██▍                                                                       | 3220/100000 [07:20<3:27:15,  7.78it/s]
  3%|██▍                                                                       | 3225/100000 [07:20<3:53:00,  6.92it/s]
  3%|██▍                                                                       | 3230/100000 [07:21<3:27:11,  7.78it/s]
  3%|██▍                                                                       | 3235/100000 [07:22<3:53:06,  6.92it/s]
  3%|██▍                                                                       | 3240/100000 [07:22<3:27:55,  7.76it/s]
  3%|██▍                                                                       | 3245/100000 [07:23<3:54:29,  6.88it/s]
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  4%|███▏                                                                      | 4385/100000 [09:58<3:48:05,  6.99it/s]
  4%|███▏                                                                      | 4390/100000 [09:59<3:22:37,  7.86it/s]
  4%|███▎                                                                      | 4395/100000 [10:00<3:48:53,  6.96it/s]
  4%|███▎                                                                      | 4400/100000 [10:00<3:23:12,  7.84it/s]
  4%|███▎                                                                      | 4405/100000 [10:01<3:48:57,  6.96it/s]
  4%|███▎                                                                      | 4410/100000 [10:02<3:23:44,  7.82it/s]
  4%|███▎                                                                      | 4415/100000 [10:03<3:49:14,  6.95it/s]
  4%|███▎                                                                      | 4420/100000 [10:03<3:23:10,  7.84it/s]
  4%|███▎                                                                      | 4425/100000 [10:04<3:47:58,  6.99it/s]
  4%|███▎                                                                      | 4430/100000 [10:04<3:22:44,  7.86it/s]
  4%|███▎                                                                      | 4435/100000 [10:05<3:49:34,  6.94it/s]
  4%|███▎                                                                      | 4440/100000 [10:06<3:23:27,  7.83it/s]
  4%|███▎                                                                      | 4445/100000 [10:07<3:47:59,  6.99it/s]
  4%|███▎                                                                      | 4450/100000 [10:07<3:22:24,  7.87it/s]
  4%|███▎                                                                      | 4455/100000 [10:08<3:47:20,  7.00it/s]
  4%|███▎                                                                      | 4460/100000 [10:08<3:22:12,  7.87it/s]
  4%|███▎                                                                      | 4465/100000 [10:09<3:48:14,  6.98it/s]
  4%|███▎                                                                      | 4470/100000 [10:10<3:22:18,  7.87it/s]
  4%|███▎                                                                      | 4475/100000 [10:11<3:47:52,  6.99it/s]
  4%|███▎                                                                      | 4480/100000 [10:11<3:22:27,  7.86it/s]
  4%|███▎                                                                      | 4485/100000 [10:12<3:47:57,  6.98it/s]
  4%|███▎                                                                      | 4490/100000 [10:12<3:22:25,  7.86it/s]
  4%|███▎                                                                      | 4495/100000 [10:13<3:47:04,  7.01it/s]
  4%|███▎                                                                      | 4500/100000 [10:14<3:21:46,  7.89it/s]
  5%|███▎                                                                      | 4505/100000 [10:15<3:46:31,  7.03it/s]
  5%|███▎                                                                      | 4510/100000 [10:15<3:21:29,  7.90it/s]
  5%|███▎                                                                      | 4515/100000 [10:16<3:46:59,  7.01it/s]
  5%|███▎                                                                      | 4520/100000 [10:16<3:21:31,  7.90it/s]
  5%|███▎                                                                      | 4525/100000 [10:17<3:47:06,  7.01it/s]
  5%|███▎                                                                      | 4530/100000 [10:18<3:22:03,  7.87it/s]
  5%|███▎                                                                      | 4535/100000 [10:19<3:47:49,  6.98it/s]
  5%|███▎                                                                      | 4540/100000 [10:19<3:22:02,  7.87it/s]
  5%|███▎                                                                      | 4545/100000 [10:20<3:46:45,  7.02it/s]
  5%|███▎                                                                      | 4550/100000 [10:21<3:21:34,  7.89it/s]
  5%|███▎                                                                      | 4555/100000 [10:21<3:46:34,  7.02it/s]
  5%|███▎                                                                      | 4560/100000 [10:22<3:21:14,  7.90it/s]
  5%|███▍                                                                      | 4565/100000 [10:23<3:47:09,  7.00it/s]
  5%|███▍                                                                      | 4570/100000 [10:23<3:21:40,  7.89it/s]
  5%|███▍                                                                      | 4575/100000 [10:24<3:47:16,  7.00it/s]
  5%|███▍                                                                      | 4580/100000 [10:25<3:21:24,  7.90it/s]
  5%|███▍                                                                      | 4585/100000 [10:25<3:45:58,  7.04it/s]
  5%|███▍                                                                      | 4590/100000 [10:26<3:20:48,  7.92it/s]
  5%|███▍                                                                      | 4595/100000 [10:27<3:46:44,  7.01it/s]
  5%|███▍                                                                      | 4600/100000 [10:27<3:21:41,  7.88it/s]
  5%|███▍                                                                      | 4605/100000 [10:28<3:47:00,  7.00it/s]
  5%|███▍                                                                      | 4610/100000 [10:29<3:21:34,  7.89it/s]
  5%|███▍                                                                      | 4615/100000 [10:30<3:47:03,  7.00it/s]
  5%|███▍                                                                      | 4620/100000 [10:30<3:21:15,  7.90it/s]
  5%|███▍                                                                      | 4625/100000 [10:31<3:46:18,  7.02it/s]
  5%|███▍                                                                      | 4630/100000 [10:31<3:21:10,  7.90it/s]
  5%|███▍                                                                      | 4635/100000 [10:32<3:46:02,  7.03it/s]
  5%|███▍                                                                      | 4640/100000 [10:33<3:20:50,  7.91it/s]
  5%|███▍                                                                      | 4645/100000 [10:34<3:46:10,  7.03it/s]
  5%|███▍                                                                      | 4650/100000 [10:34<3:20:53,  7.91it/s]
  5%|███▍                                                                      | 4655/100000 [10:35<3:47:14,  6.99it/s]
  5%|███▍                                                                      | 4660/100000 [10:35<3:21:32,  7.88it/s]
  5%|███▍                                                                      | 4665/100000 [10:36<3:47:25,  6.99it/s]
  5%|███▍                                                                      | 4670/100000 [10:37<3:21:45,  7.88it/s]
  5%|███▍                                                                      | 4675/100000 [10:38<3:49:05,  6.93it/s]
  5%|███▍                                                                      | 4680/100000 [10:38<3:22:34,  7.84it/s]
  5%|███▍                                                                      | 4685/100000 [10:39<3:48:28,  6.95it/s]
  5%|███▍                                                                      | 4690/100000 [10:39<3:22:30,  7.84it/s]
  5%|███▍                                                                      | 4695/100000 [10:40<3:46:33,  7.01it/s]
  5%|███▍                                                                      | 4700/100000 [10:41<3:21:09,  7.90it/s]
  5%|███▍                                                                      | 4705/100000 [10:42<3:45:49,  7.03it/s]
  5%|███▍                                                                      | 4710/100000 [10:42<3:20:40,  7.91it/s]
  5%|███▍                                                                      | 4715/100000 [10:43<3:45:36,  7.04it/s]
  5%|███▍                                                                      | 4720/100000 [10:43<3:20:05,  7.94it/s]
  5%|███▍                                                                      | 4725/100000 [10:44<3:45:21,  7.05it/s]
  5%|███▌                                                                      | 4730/100000 [10:45<3:20:05,  7.94it/s]
  5%|███▌                                                                      | 4735/100000 [10:46<3:46:52,  7.00it/s]
  5%|███▌                                                                      | 4740/100000 [10:46<3:21:31,  7.88it/s]
  5%|███▌                                                                      | 4745/100000 [10:47<3:46:13,  7.02it/s]
  5%|███▌                                                                      | 4750/100000 [10:47<3:21:10,  7.89it/s]
  5%|███▌                                                                      | 4755/100000 [10:48<3:47:05,  6.99it/s]
  5%|███▌                                                                      | 4760/100000 [10:49<3:21:24,  7.88it/s]
  5%|███▌                                                                      | 4765/100000 [10:50<3:46:43,  7.00it/s]
  5%|███▌                                                                      | 4770/100000 [10:50<3:21:35,  7.87it/s]
  5%|███▌                                                                      | 4775/100000 [10:51<3:47:17,  6.98it/s]
  5%|███▌                                                                      | 4780/100000 [10:52<3:21:21,  7.88it/s]
  5%|███▌                                                                      | 4785/100000 [10:52<3:46:33,  7.00it/s]
  5%|███▌                                                                      | 4790/100000 [10:53<3:21:02,  7.89it/s]
  5%|███▌                                                                      | 4795/100000 [10:54<3:47:50,  6.96it/s]
  5%|███▌                                                                      | 4800/100000 [10:54<3:22:11,  7.85it/s]
  5%|███▌                                                                      | 4805/100000 [10:55<3:46:58,  6.99it/s]
  5%|███▌                                                                      | 4810/100000 [10:56<3:21:19,  7.88it/s]
  5%|███▌                                                                      | 4815/100000 [10:56<3:47:19,  6.98it/s]
  5%|███▌                                                                      | 4820/100000 [10:57<3:21:45,  7.86it/s]
  5%|███▌                                                                      | 4825/100000 [10:58<3:46:02,  7.02it/s]
  5%|███▌                                                                      | 4830/100000 [10:58<3:20:46,  7.90it/s]
  5%|███▌                                                                      | 4835/100000 [10:59<3:45:46,  7.02it/s]
  5%|███▌                                                                      | 4840/100000 [11:00<3:20:30,  7.91it/s]
  5%|███▌                                                                      | 4845/100000 [11:01<3:46:04,  7.01it/s]
  5%|███▌                                                                      | 4850/100000 [11:01<3:20:33,  7.91it/s]
  5%|███▌                                                                      | 4855/100000 [11:02<3:45:45,  7.02it/s]
  5%|███▌                                                                      | 4860/100000 [11:02<3:20:31,  7.91it/s]
  5%|███▌                                                                      | 4865/100000 [11:03<3:45:45,  7.02it/s]
  5%|███▌                                                                      | 4870/100000 [11:04<3:20:03,  7.93it/s]
  5%|███▌                                                                      | 4875/100000 [11:05<3:44:50,  7.05it/s]
  5%|███▌                                                                      | 4880/100000 [11:05<3:19:13,  7.96it/s]
  5%|███▌                                                                      | 4885/100000 [11:06<3:43:51,  7.08it/s]
  5%|███▌                                                                      | 4890/100000 [11:06<3:19:03,  7.96it/s]
  5%|███▌                                                                      | 4895/100000 [11:07<3:44:32,  7.06it/s]
  5%|███▋                                                                      | 4900/100000 [11:08<3:19:36,  7.94it/s]
  5%|███▋                                                                      | 4905/100000 [11:09<3:43:57,  7.08it/s]
  5%|███▋                                                                      | 4910/100000 [11:09<3:19:00,  7.96it/s]
  5%|███▋                                                                      | 4915/100000 [11:10<3:44:25,  7.06it/s]
  5%|███▋                                                                      | 4920/100000 [11:10<3:19:16,  7.95it/s]
  5%|███▋                                                                      | 4925/100000 [11:11<3:44:15,  7.07it/s]
  5%|███▋                                                                      | 4930/100000 [11:12<3:19:41,  7.94it/s]
  5%|███▋                                                                      | 4935/100000 [11:13<3:43:58,  7.07it/s]
  5%|███▋                                                                      | 4940/100000 [11:13<3:19:02,  7.96it/s]
  5%|███▋                                                                      | 4945/100000 [11:14<3:45:50,  7.01it/s]
  5%|███▋                                                                      | 4950/100000 [11:14<3:21:18,  7.87it/s]
  5%|███▋                                                                      | 4955/100000 [11:15<3:48:09,  6.94it/s]
  5%|███▋                                                                      | 4960/100000 [11:16<3:22:38,  7.82it/s]
  5%|███▋                                                                      | 4965/100000 [11:17<3:47:51,  6.95it/s]
  5%|███▋                                                                      | 4970/100000 [11:17<3:24:50,  7.73it/s]
  5%|███▋                                                                      | 4975/100000 [11:18<3:48:29,  6.93it/s]
  5%|███▋                                                                      | 4980/100000 [11:18<3:22:13,  7.83it/s]
  5%|███▋                                                                      | 4985/100000 [11:19<3:46:23,  6.99it/s]
  5%|███▋                                                                      | 4990/100000 [11:20<3:21:04,  7.88it/s]
  5%|███▋                                                                      | 4995/100000 [11:21<3:46:26,  6.99it/s]
  5%|███▋                                                                      | 5000/100000 [11:21<3:21:34,  7.85it/s]
  5%|███▋                                                                      | 5005/100000 [11:22<3:45:55,  7.01it/s]
  5%|███▋                                                                      | 5010/100000 [11:22<3:20:14,  7.91it/s]
  5%|███▋                                                                      | 5015/100000 [11:23<3:44:35,  7.05it/s]
  5%|███▋                                                                      | 5020/100000 [11:24<3:20:52,  7.88it/s]
  5%|███▋                                                                      | 5025/100000 [11:25<3:46:36,  6.99it/s]
  5%|███▋                                                                      | 5030/100000 [11:25<3:20:35,  7.89it/s]
  5%|███▋                                                                      | 5035/100000 [11:26<3:44:39,  7.05it/s]
  5%|███▋                                                                      | 5040/100000 [11:27<3:19:52,  7.92it/s]
  5%|███▋                                                                      | 5045/100000 [11:27<3:45:53,  7.01it/s]
  5%|███▋                                                                      | 5050/100000 [11:28<3:20:32,  7.89it/s]
  5%|███▋                                                                      | 5055/100000 [11:29<3:45:50,  7.01it/s]
  5%|███▋                                                                      | 5060/100000 [11:29<3:20:28,  7.89it/s]
  5%|███▋                                                                      | 5065/100000 [11:30<3:46:02,  7.00it/s]
  5%|███▊                                                                      | 5070/100000 [11:31<3:20:31,  7.89it/s]
  5%|███▊                                                                      | 5075/100000 [11:31<3:46:01,  7.00it/s]
  5%|███▊                                                                      | 5080/100000 [11:32<3:20:26,  7.89it/s]
  5%|███▊                                                                      | 5085/100000 [11:33<3:44:45,  7.04it/s]
  5%|███▊                                                                      | 5090/100000 [11:33<3:20:14,  7.90it/s]
  5%|███▊                                                                      | 5095/100000 [11:34<3:44:50,  7.03it/s]
  5%|███▊                                                                      | 5100/100000 [11:35<3:19:27,  7.93it/s]
  5%|███▊                                                                      | 5105/100000 [11:35<3:44:26,  7.05it/s]
  5%|███▊                                                                      | 5110/100000 [11:36<3:19:46,  7.92it/s]
  5%|███▊                                                                      | 5115/100000 [11:37<3:45:44,  7.01it/s]
  5%|███▊                                                                      | 5120/100000 [11:37<3:20:17,  7.90it/s]
  5%|███▊                                                                      | 5125/100000 [11:38<3:45:58,  7.00it/s]
  5%|███▊                                                                      | 5130/100000 [11:39<3:20:52,  7.87it/s]
  5%|███▊                                                                      | 5135/100000 [11:40<3:45:46,  7.00it/s]
  5%|███▊                                                                      | 5140/100000 [11:40<3:20:01,  7.90it/s]
  5%|███▊                                                                      | 5145/100000 [11:41<3:44:14,  7.05it/s]
  5%|███▊                                                                      | 5150/100000 [11:41<3:18:57,  7.95it/s]
  5%|███▊                                                                      | 5155/100000 [11:42<3:45:14,  7.02it/s]
  5%|███▊                                                                      | 5160/100000 [11:43<3:19:54,  7.91it/s]
  5%|███▊                                                                      | 5165/100000 [11:44<3:44:28,  7.04it/s]
  5%|███▊                                                                      | 5170/100000 [11:44<3:20:15,  7.89it/s]
  5%|███▊                                                                      | 5175/100000 [11:45<3:45:52,  7.00it/s]
  5%|███▊                                                                      | 5180/100000 [11:45<3:20:29,  7.88it/s]
  5%|███▊                                                                      | 5185/100000 [11:46<3:45:12,  7.02it/s]
  5%|███▊                                                                      | 5190/100000 [11:47<3:20:35,  7.88it/s]
  5%|███▊                                                                      | 5195/100000 [11:48<3:44:02,  7.05it/s]
  5%|███▊                                                                      | 5200/100000 [11:48<3:18:53,  7.94it/s]
  5%|███▊                                                                      | 5205/100000 [11:49<3:44:16,  7.04it/s]
  5%|███▊                                                                      | 5210/100000 [11:49<3:19:14,  7.93it/s]
  5%|███▊                                                                      | 5215/100000 [11:50<3:44:35,  7.03it/s]
  5%|███▊                                                                      | 5220/100000 [11:51<3:19:36,  7.91it/s]
  5%|███▊                                                                      | 5225/100000 [11:52<3:43:38,  7.06it/s]
  5%|███▊                                                                      | 5230/100000 [11:52<3:18:48,  7.94it/s]
  5%|███▊                                                                      | 5235/100000 [11:53<3:44:21,  7.04it/s]
  5%|███▉                                                                      | 5240/100000 [11:53<3:19:41,  7.91it/s]
  5%|███▉                                                                      | 5245/100000 [11:54<3:45:34,  7.00it/s]
  5%|███▉                                                                      | 5250/100000 [11:55<3:20:04,  7.89it/s]
  5%|███▉                                                                      | 5255/100000 [11:56<3:45:49,  6.99it/s]
  5%|███▉                                                                      | 5260/100000 [11:56<3:20:46,  7.86it/s]
  5%|███▉                                                                      | 5265/100000 [11:57<3:45:26,  7.00it/s]
  5%|███▉                                                                      | 5270/100000 [11:57<3:19:45,  7.90it/s]
  5%|███▉                                                                      | 5275/100000 [11:58<3:44:39,  7.03it/s]
  5%|███▉                                                                      | 5280/100000 [11:59<3:19:08,  7.93it/s]
  5%|███▉                                                                      | 5285/100000 [12:00<3:43:32,  7.06it/s]
  5%|███▉                                                                      | 5290/100000 [12:00<3:21:04,  7.85it/s]
  5%|███▉                                                                      | 5295/100000 [12:01<3:44:12,  7.04it/s]
  5%|███▉                                                                      | 5300/100000 [12:01<3:18:47,  7.94it/s]
  5%|███▉                                                                      | 5305/100000 [12:02<3:43:00,  7.08it/s]
  5%|███▉                                                                      | 5310/100000 [12:03<3:18:00,  7.97it/s]
  5%|███▉                                                                      | 5315/100000 [12:04<3:42:56,  7.08it/s]
  5%|███▉                                                                      | 5320/100000 [12:04<3:17:59,  7.97it/s]
  5%|███▉                                                                      | 5325/100000 [12:05<3:43:38,  7.06it/s]
  5%|███▉                                                                      | 5330/100000 [12:05<3:18:44,  7.94it/s]
  5%|███▉                                                                      | 5335/100000 [12:06<3:44:55,  7.01it/s]
  5%|███▉                                                                      | 5340/100000 [12:07<3:19:24,  7.91it/s]
  5%|███▉                                                                      | 5345/100000 [12:08<3:44:12,  7.04it/s]
  5%|███▉                                                                      | 5350/100000 [12:08<3:18:53,  7.93it/s]
  5%|███▉                                                                      | 5355/100000 [12:09<3:44:55,  7.01it/s]
  5%|███▉                                                                      | 5360/100000 [12:10<3:20:06,  7.88it/s]
  5%|███▉                                                                      | 5365/100000 [12:10<3:44:25,  7.03it/s]
  5%|███▉                                                                      | 5370/100000 [12:11<3:19:56,  7.89it/s]
  5%|███▉                                                                      | 5375/100000 [12:12<3:44:19,  7.03it/s]
  5%|███▉                                                                      | 5380/100000 [12:12<3:19:07,  7.92it/s]
  5%|███▉                                                                      | 5385/100000 [12:13<3:43:41,  7.05it/s]
  5%|███▉                                                                      | 5390/100000 [12:14<3:18:22,  7.95it/s]
  5%|███▉                                                                      | 5395/100000 [12:14<3:43:28,  7.06it/s]
  5%|███▉                                                                      | 5400/100000 [12:15<3:18:15,  7.95it/s]
  5%|███▉                                                                      | 5405/100000 [12:16<3:43:33,  7.05it/s]
  5%|████                                                                      | 5410/100000 [12:16<3:18:32,  7.94it/s]
  5%|████                                                                      | 5415/100000 [12:17<3:43:37,  7.05it/s]
  5%|████                                                                      | 5420/100000 [12:18<3:18:08,  7.96it/s]
  5%|████                                                                      | 5425/100000 [12:18<3:43:08,  7.06it/s]
  5%|████                                                                      | 5430/100000 [12:19<3:18:12,  7.95it/s]
  5%|████                                                                      | 5435/100000 [12:20<3:42:50,  7.07it/s]
  5%|████                                                                      | 5440/100000 [12:20<3:18:04,  7.96it/s]
  5%|████                                                                      | 5445/100000 [12:21<3:43:21,  7.06it/s]
  5%|████                                                                      | 5450/100000 [12:22<3:18:27,  7.94it/s]
  5%|████                                                                      | 5455/100000 [12:22<3:43:44,  7.04it/s]
  5%|████                                                                      | 5460/100000 [12:23<3:19:26,  7.90it/s]
  5%|████                                                                      | 5465/100000 [12:24<3:44:58,  7.00it/s]
  5%|████                                                                      | 5470/100000 [12:24<3:19:34,  7.89it/s]
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 14%|█████████▌                                                             | 13555/100000 [1:12:39<3:06:58,  7.71it/s]
 14%|█████████▋                                                             | 13560/100000 [1:12:40<2:45:55,  8.68it/s]
 14%|█████████▋                                                             | 13565/100000 [1:12:40<3:06:49,  7.71it/s]
 14%|█████████▋                                                             | 13570/100000 [1:12:41<2:45:59,  8.68it/s]
 14%|█████████▋                                                             | 13575/100000 [1:12:42<3:06:59,  7.70it/s]
 14%|█████████▋                                                             | 13580/100000 [1:12:42<2:46:08,  8.67it/s]
 14%|█████████▋                                                             | 13585/100000 [1:12:43<3:06:41,  7.71it/s]
 14%|█████████▋                                                             | 13590/100000 [1:12:43<2:45:32,  8.70it/s]
 14%|█████████▋                                                             | 13595/100000 [1:12:44<3:06:26,  7.72it/s]
 14%|█████████▋                                                             | 13600/100000 [1:12:44<2:46:04,  8.67it/s]
 14%|█████████▋                                                             | 13605/100000 [1:12:45<3:07:13,  7.69it/s]
 14%|█████████▋                                                             | 13610/100000 [1:12:46<2:46:39,  8.64it/s]
 14%|█████████▋                                                             | 13615/100000 [1:12:47<3:06:56,  7.70it/s]
 14%|█████████▋                                                             | 13620/100000 [1:12:47<2:46:07,  8.67it/s]
 14%|█████████▋                                                             | 13625/100000 [1:12:48<3:09:21,  7.60it/s]
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 14%|█████████▋                                                             | 13635/100000 [1:12:49<3:07:47,  7.67it/s]
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 14%|█████████▋                                                             | 13655/100000 [1:12:51<3:06:53,  7.70it/s]
 14%|█████████▋                                                             | 13660/100000 [1:12:52<2:45:57,  8.67it/s]
 14%|█████████▋                                                             | 13665/100000 [1:12:53<3:06:31,  7.71it/s]
 14%|█████████▋                                                             | 13670/100000 [1:12:53<2:45:37,  8.69it/s]
 14%|█████████▋                                                             | 13675/100000 [1:12:54<3:07:27,  7.68it/s]
 14%|█████████▋                                                             | 13680/100000 [1:12:54<2:46:27,  8.64it/s]
 14%|█████████▋                                                             | 13685/100000 [1:12:55<3:07:02,  7.69it/s]
 14%|█████████▋                                                             | 13690/100000 [1:12:56<2:46:06,  8.66it/s]
 14%|█████████▋                                                             | 13695/100000 [1:12:56<3:07:01,  7.69it/s]
 14%|█████████▋                                                             | 13700/100000 [1:12:57<2:46:00,  8.66it/s]
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 14%|█████████▊                                                             | 13735/100000 [1:13:01<3:07:27,  7.67it/s]
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 14%|█████████▊                                                             | 13760/100000 [1:13:04<2:46:00,  8.66it/s]
 14%|█████████▊                                                             | 13765/100000 [1:13:05<3:06:34,  7.70it/s]
 14%|█████████▊                                                             | 13770/100000 [1:13:05<2:46:14,  8.65it/s]
 14%|█████████▊                                                             | 13775/100000 [1:13:06<3:05:59,  7.73it/s]
 14%|█████████▊                                                             | 13780/100000 [1:13:07<2:45:22,  8.69it/s]
 14%|█████████▊                                                             | 13785/100000 [1:13:07<3:06:24,  7.71it/s]
 14%|█████████▊                                                             | 13790/100000 [1:13:08<2:45:29,  8.68it/s]
 14%|█████████▊                                                             | 13795/100000 [1:13:09<3:05:45,  7.73it/s]
 14%|█████████▊                                                             | 13800/100000 [1:13:09<2:45:07,  8.70it/s]
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 14%|█████████▊                                                             | 13810/100000 [1:13:10<2:45:04,  8.70it/s]
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 14%|█████████▊                                                             | 13825/100000 [1:13:12<3:05:59,  7.72it/s]
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 14%|█████████▊                                                             | 13835/100000 [1:13:13<3:05:35,  7.74it/s]
 14%|█████████▊                                                             | 13840/100000 [1:13:14<2:45:09,  8.70it/s]
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 93%|███████████████████████████████████████████████████████████████████▎    | 93495/100000 [1:55:37<00:27, 237.55it/s]
 94%|███████████████████████████████████████████████████████████████████▎    | 93525/100000 [1:55:37<00:27, 238.53it/s]
 94%|███████████████████████████████████████████████████████████████████▎    | 93555/100000 [1:55:38<00:26, 242.04it/s]
 94%|███████████████████████████████████████████████████████████████████▍    | 93585/100000 [1:55:38<00:26, 245.31it/s]
 94%|███████████████████████████████████████████████████████████████████▍    | 93615/100000 [1:55:38<00:26, 245.31it/s]
 94%|███████████████████████████████████████████████████████████████████▍    | 93645/100000 [1:55:38<00:25, 245.12it/s]
 94%|███████████████████████████████████████████████████████████████████▍    | 93675/100000 [1:55:38<00:25, 248.77it/s]
 94%|███████████████████████████████████████████████████████████████████▍    | 93705/100000 [1:55:38<00:24, 253.86it/s]
 94%|███████████████████████████████████████████████████████████████████▍    | 93735/100000 [1:55:38<00:24, 259.27it/s]
 94%|███████████████████████████████████████████████████████████████████▌    | 93765/100000 [1:55:38<00:23, 262.62it/s]
 94%|███████████████████████████████████████████████████████████████████▌    | 93795/100000 [1:55:38<00:23, 264.65it/s]
 94%|███████████████████████████████████████████████████████████████████▌    | 93825/100000 [1:55:39<00:22, 271.37it/s]
 94%|███████████████████████████████████████████████████████████████████▌    | 93855/100000 [1:55:39<00:22, 269.56it/s]
 94%|███████████████████████████████████████████████████████████████████▌    | 93885/100000 [1:55:39<00:23, 263.10it/s]
 94%|███████████████████████████████████████████████████████████████████▌    | 93915/100000 [1:55:39<00:23, 264.10it/s]
 94%|███████████████████████████████████████████████████████████████████▋    | 93945/100000 [1:55:39<00:22, 265.56it/s]
 94%|███████████████████████████████████████████████████████████████████▋    | 93975/100000 [1:55:39<00:22, 267.19it/s]
 94%|███████████████████████████████████████████████████████████████████▋    | 94005/100000 [1:55:39<00:22, 267.03it/s]
 94%|███████████████████████████████████████████████████████████████████▋    | 94035/100000 [1:55:39<00:22, 268.62it/s]
 94%|███████████████████████████████████████████████████████████████████▋    | 94065/100000 [1:55:39<00:21, 272.78it/s]
 94%|███████████████████████████████████████████████████████████████████▋    | 94095/100000 [1:55:40<00:21, 278.43it/s]
 94%|███████████████████████████████████████████████████████████████████▊    | 94125/100000 [1:55:40<00:21, 275.62it/s]
 94%|███████████████████████████████████████████████████████████████████▊    | 94155/100000 [1:55:40<00:20, 279.33it/s]
 94%|███████████████████████████████████████████████████████████████████▊    | 94185/100000 [1:55:40<00:20, 283.35it/s]
 94%|███████████████████████████████████████████████████████████████████▊    | 94220/100000 [1:55:40<00:19, 293.02it/s]
 94%|███████████████████████████████████████████████████████████████████▊    | 94250/100000 [1:55:40<00:19, 291.13it/s]
 94%|███████████████████████████████████████████████████████████████████▉    | 94280/100000 [1:55:40<00:19, 290.99it/s]
 94%|███████████████████████████████████████████████████████████████████▉    | 94310/100000 [1:55:40<00:19, 289.30it/s]
 94%|███████████████████████████████████████████████████████████████████▉    | 94345/100000 [1:55:40<00:19, 291.50it/s]
 94%|███████████████████████████████████████████████████████████████████▉    | 94375/100000 [1:55:41<00:19, 293.42it/s]
 94%|███████████████████████████████████████████████████████████████████▉    | 94410/100000 [1:55:41<00:18, 305.78it/s]
 94%|████████████████████████████████████████████████████████████████████    | 94445/100000 [1:55:41<00:18, 293.46it/s]
 94%|████████████████████████████████████████████████████████████████████    | 94480/100000 [1:55:41<00:18, 304.00it/s]
 95%|████████████████████████████████████████████████████████████████████    | 94515/100000 [1:55:41<00:18, 299.74it/s]
 95%|████████████████████████████████████████████████████████████████████    | 94550/100000 [1:55:41<00:17, 306.84it/s]
 95%|████████████████████████████████████████████████████████████████████    | 94585/100000 [1:55:41<00:17, 304.53it/s]
 95%|████████████████████████████████████████████████████████████████████▏   | 94620/100000 [1:55:41<00:17, 314.15it/s]
 95%|████████████████████████████████████████████████████████████████████▏   | 94655/100000 [1:55:41<00:17, 313.13it/s]
 95%|████████████████████████████████████████████████████████████████████▏   | 94690/100000 [1:55:42<00:16, 316.35it/s]
 95%|████████████████████████████████████████████████████████████████████▏   | 94725/100000 [1:55:42<00:16, 312.38it/s]
 95%|████████████████████████████████████████████████████████████████████▏   | 94760/100000 [1:55:42<00:16, 311.50it/s]
 95%|████████████████████████████████████████████████████████████████████▎   | 94795/100000 [1:55:42<00:16, 312.30it/s]
 95%|████████████████████████████████████████████████████████████████████▎   | 94835/100000 [1:55:42<00:16, 311.82it/s]
 95%|████████████████████████████████████████████████████████████████████▎   | 94870/100000 [1:55:42<00:16, 315.21it/s]
 95%|████████████████████████████████████████████████████████████████████▎   | 94905/100000 [1:55:42<00:16, 318.35it/s]
 95%|████████████████████████████████████████████████████████████████████▎   | 94945/100000 [1:55:42<00:15, 320.31it/s]
 95%|████████████████████████████████████████████████████████████████████▍   | 94985/100000 [1:55:42<00:15, 324.94it/s]
 95%|████████████████████████████████████████████████████████████████████▍   | 95025/100000 [1:55:43<00:14, 331.77it/s]
 95%|████████████████████████████████████████████████████████████████████▍   | 95065/100000 [1:55:43<00:14, 337.95it/s]
 95%|████████████████████████████████████████████████████████████████████▍   | 95105/100000 [1:55:43<00:14, 341.90it/s]
 95%|████████████████████████████████████████████████████████████████████▌   | 95145/100000 [1:55:43<00:14, 341.70it/s]
 95%|████████████████████████████████████████████████████████████████████▌   | 95180/100000 [1:55:43<00:14, 341.03it/s]
 95%|████████████████████████████████████████████████████████████████████▌   | 95215/100000 [1:55:43<00:14, 339.98it/s]
 95%|████████████████████████████████████████████████████████████████████▌   | 95255/100000 [1:55:43<00:13, 341.48it/s]
 95%|████████████████████████████████████████████████████████████████████▌   | 95295/100000 [1:55:43<00:13, 348.38it/s]
 95%|████████████████████████████████████████████████████████████████████▋   | 95335/100000 [1:55:43<00:13, 348.30it/s]
 95%|████████████████████████████████████████████████████████████████████▋   | 95375/100000 [1:55:44<00:13, 351.78it/s]
 95%|████████████████████████████████████████████████████████████████████▋   | 95415/100000 [1:55:44<00:12, 355.69it/s]
 95%|████████████████████████████████████████████████████████████████████▋   | 95455/100000 [1:55:44<00:12, 353.76it/s]
 95%|████████████████████████████████████████████████████████████████████▊   | 95495/100000 [1:55:44<00:12, 358.53it/s]
 96%|████████████████████████████████████████████████████████████████████▊   | 95535/100000 [1:55:44<00:12, 362.76it/s]
 96%|████████████████████████████████████████████████████████████████████▊   | 95575/100000 [1:55:44<00:12, 368.19it/s]
 96%|████████████████████████████████████████████████████████████████████▊   | 95615/100000 [1:55:44<00:11, 375.59it/s]
 96%|████████████████████████████████████████████████████████████████████▉   | 95660/100000 [1:55:44<00:11, 388.90it/s]
 96%|████████████████████████████████████████████████████████████████████▉   | 95705/100000 [1:55:44<00:10, 391.71it/s]
 96%|████████████████████████████████████████████████████████████████████▉   | 95750/100000 [1:55:45<00:10, 399.12it/s]
 96%|████████████████████████████████████████████████████████████████████▉   | 95790/100000 [1:55:45<00:10, 391.14it/s]
 96%|█████████████████████████████████████████████████████████████████████   | 95835/100000 [1:55:45<00:10, 394.83it/s]
 96%|█████████████████████████████████████████████████████████████████████   | 95880/100000 [1:55:45<00:10, 405.98it/s]
 96%|█████████████████████████████████████████████████████████████████████   | 95925/100000 [1:55:45<00:10, 382.45it/s]
 96%|█████████████████████████████████████████████████████████████████████   | 95970/100000 [1:55:45<00:10, 394.70it/s]
 96%|█████████████████████████████████████████████████████████████████████▏  | 96010/100000 [1:55:45<00:10, 390.84it/s]
 96%|█████████████████████████████████████████████████████████████████████▏  | 96055/100000 [1:55:45<00:09, 399.60it/s]
 96%|█████████████████████████████████████████████████████████████████████▏  | 96100/100000 [1:55:45<00:09, 412.95it/s]
 96%|█████████████████████████████████████████████████████████████████████▏  | 96145/100000 [1:55:46<00:09, 406.80it/s]
 96%|█████████████████████████████████████████████████████████████████████▎  | 96190/100000 [1:55:46<00:09, 407.72it/s]
 96%|█████████████████████████████████████████████████████████████████████▎  | 96240/100000 [1:55:46<00:08, 426.46it/s]
 96%|█████████████████████████████████████████████████████████████████████▎  | 96285/100000 [1:55:46<00:08, 431.78it/s]
 96%|█████████████████████████████████████████████████████████████████████▎  | 96335/100000 [1:55:46<00:08, 433.49it/s]
 96%|█████████████████████████████████████████████████████████████████████▍  | 96380/100000 [1:55:46<00:08, 434.57it/s]
 96%|█████████████████████████████████████████████████████████████████████▍  | 96425/100000 [1:55:46<00:08, 434.22it/s]
 96%|█████████████████████████████████████████████████████████████████████▍  | 96475/100000 [1:55:46<00:08, 437.24it/s]
 97%|█████████████████████████████████████████████████████████████████████▍  | 96525/100000 [1:55:46<00:07, 447.53it/s]
 97%|█████████████████████████████████████████████████████████████████████▌  | 96575/100000 [1:55:46<00:07, 458.66it/s]
 97%|█████████████████████████████████████████████████████████████████████▌  | 96630/100000 [1:55:47<00:07, 478.74it/s]
 97%|█████████████████████████████████████████████████████████████████████▌  | 96685/100000 [1:55:47<00:06, 483.31it/s]
 97%|█████████████████████████████████████████████████████████████████████▋  | 96735/100000 [1:55:47<00:06, 475.43it/s]
 97%|█████████████████████████████████████████████████████████████████████▋  | 96785/100000 [1:55:47<00:06, 475.98it/s]
 97%|█████████████████████████████████████████████████████████████████████▋  | 96845/100000 [1:55:47<00:06, 497.36it/s]
 97%|█████████████████████████████████████████████████████████████████████▊  | 96905/100000 [1:55:47<00:06, 508.49it/s]
 97%|█████████████████████████████████████████████████████████████████████▊  | 96960/100000 [1:55:47<00:05, 510.46it/s]
 97%|█████████████████████████████████████████████████████████████████████▊  | 97015/100000 [1:55:47<00:05, 514.73it/s]
 97%|█████████████████████████████████████████████████████████████████████▉  | 97075/100000 [1:55:47<00:05, 527.24it/s]
 97%|█████████████████████████████████████████████████████████████████████▉  | 97140/100000 [1:55:48<00:05, 555.75it/s]
 97%|█████████████████████████████████████████████████████████████████████▉  | 97205/100000 [1:55:48<00:04, 568.10it/s]
 97%|██████████████████████████████████████████████████████████████████████  | 97265/100000 [1:55:48<00:04, 567.93it/s]
 97%|██████████████████████████████████████████████████████████████████████  | 97330/100000 [1:55:48<00:04, 587.37it/s]
 97%|██████████████████████████████████████████████████████████████████████  | 97390/100000 [1:55:48<00:04, 585.64it/s]
 97%|██████████████████████████████████████████████████████████████████████▏ | 97455/100000 [1:55:48<00:04, 588.35it/s]
 98%|██████████████████████████████████████████████████████████████████████▏ | 97520/100000 [1:55:48<00:04, 605.90it/s]
 98%|██████████████████████████████████████████████████████████████████████▎ | 97595/100000 [1:55:48<00:03, 634.08it/s]
 98%|██████████████████████████████████████████████████████████████████████▎ | 97665/100000 [1:55:48<00:03, 651.63it/s]
 98%|██████████████████████████████████████████████████████████████████████▎ | 97735/100000 [1:55:49<00:03, 664.88it/s]
 98%|██████████████████████████████████████████████████████████████████████▍ | 97810/100000 [1:55:49<00:03, 688.73it/s]
 98%|██████████████████████████████████████████████████████████████████████▍ | 97890/100000 [1:55:49<00:02, 718.87it/s]
 98%|██████████████████████████████████████████████████████████████████████▌ | 97975/100000 [1:55:49<00:02, 754.50it/s]
 98%|██████████████████████████████████████████████████████████████████████▌ | 98065/100000 [1:55:49<00:02, 792.01it/s]
 98%|██████████████████████████████████████████████████████████████████████▋ | 98165/100000 [1:55:49<00:02, 840.34it/s]
 98%|██████████████████████████████████████████████████████████████████████▋ | 98255/100000 [1:55:49<00:02, 857.71it/s]
 98%|██████████████████████████████████████████████████████████████████████▊ | 98360/100000 [1:55:49<00:01, 908.71it/s]
 98%|██████████████████████████████████████████████████████████████████████▉ | 98470/100000 [1:55:49<00:01, 957.62it/s]
 99%|██████████████████████████████████████████████████████████████████████▉ | 98580/100000 [1:55:49<00:01, 998.62it/s]
 99%|██████████████████████████████████████████████████████████████████████ | 98705/100000 [1:55:50<00:01, 1060.72it/s]
 99%|██████████████████████████████████████████████████████████████████████▏| 98840/100000 [1:55:50<00:01, 1141.40it/s]
 99%|██████████████████████████████████████████████████████████████████████▎| 98995/100000 [1:55:50<00:00, 1255.22it/s]
 99%|██████████████████████████████████████████████████████████████████████▍| 99180/100000 [1:55:50<00:00, 1415.20it/s]
 99%|██████████████████████████████████████████████████████████████████████▌| 99400/100000 [1:55:50<00:00, 1638.42it/s]
100%|██████████████████████████████████████████████████████████████████████▊| 99780/100000 [1:55:50<00:00, 2275.67it/s]
100%|████████████████████████████████████████████████████████████████████████| 100000/100000 [1:55:50<00:00, 14.39it/s]

Number of clusters: 20000
Mean of mean distances to centroids: 0.01394545243309274

ALTERNATIVE IMPLEMENTATION#

Substituting list comprehensions by NumPy automatic operand broadcast.

from tqdm import tqdm

def dist(x,y):
    return np.linalg.norm(x-y, axis=1)

def poprow(arr,i):
    pop = arr[i]
    new_array = np.vstack((arr[:i],arr[i+1:]))
    return new_array,pop

def cluster(X, p, k, dist_to_xr):
    c = [p]
    
    if dist_to_xr is None:
        distances = dist(p,X)
    else:
        distances = dist_to_xr
        
    X = X[np.argpartition(distances, k-1)]
    c.extend(X[:k-1])
    X = X[k-1:]
    
    return X, np.array(c)
    
def mdav(X, k):
    D = X
    clusters = []
    
    # Test feature. progress bar
    pbar = tqdm(total=len(D))
    
    while len(D) >= 3*k:
        # Centroid
        xm = np.mean(D, axis=0)
        # Furthest from centroid
        xri = np.argmax(dist(xm,D))
        D, xr = poprow(D, xri)
        # Furthest from furthest from centroid
        dist_to_xr = dist(xr,D)
        xsi = np.argmax(dist_to_xr)
        dist_to_xr = np.append(dist_to_xr[:xsi], dist_to_xr[xsi+1:], axis=0)
        D, xs = poprow(D, xsi) 

        #cluster of xr
        D, c = cluster(D, xr, k, dist_to_xr)
        clusters.append(c)
        
        # Test feature. progress bar
        pbar.update(k)
        
        #cluster of xs
        D, c = cluster(D, xs, k, None)
        clusters.append(c)
        
        # Test feature. progress bar
        pbar.update(k)
        
    if len(D) >= 2*k and len(D) < 3*k:
        # Centroid
        xm = np.mean(D, axis=0)
        # Furthest from centroid
        xri = np.argmax(dist(xm,D))
        D, xr = poprow(D, xri)
        #cluster of xr
        D, c = cluster(D, xr, k, None)
        clusters.append(c)
        
        # Test feature. progress bar
        pbar.update(k)
        
        # rest of points
        clusters.append(D[:]) 
        
        # Test feature. progress bar
        pbar.update(len(D))
        
    else:
        # rest of points
        clusters.append(D[:])
        
        # Test feature. progress bar
        pbar.update(len(D))
    
    centroids = np.array([np.mean(c,axis=0) for c in clusters], copy=False)
    
    return clusters, centroids

def print_stats(clusters, centroids):
    ss = []
    for c,cen in zip(clusters, centroids):
        #cen = np.mean(c, axis=0)
        s = np.mean(dist(cen,c), axis=0)
        ss.append(s)
        
    print(f'Number of clusters: {len(clusters)}')
    print(f'Mean of mean distances to centroids: {np.mean(ss, axis=0)}')

def plot_results(clusters):
    fig, ax = plt.subplots() 
    fig.set_size_inches(10, 10)
    for c, cen in zip(clusters, centroids):
        plt.scatter(c[:,0], c[:,1], marker='.', s=25)
        #plt.scatter(cen[0], cen[1], marker='o', s=100, edgecolor='k')
    plt.axis('off')
    plt.show()
# Vectorized MDAV
k=5
clusters, centroids = mdav(X, k)
print_stats(clusters, centroids)
plot_results(clusters)
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Number of clusters: 20000
Mean of mean distances to centroids: 0.01394545243309274
../_images/3811094068613b13a7241faf443184bb4a5e1dcdf6752a62dca5b315b1086fd8.png

STOP HERE#

k = 10000
c, cen = mdav(X, len(X) // 2)
c0, cen0 = mdav(c[0], k)
c1, cen1 = mdav(c[1], k)
clusters = np.vstack((c0,c1))
centroids = np.vstack((cen0,cen1))

print_stats(clusters, centroids)
plot_results(clusters)
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Number of clusters: 10
Mean of mean distances to centroids: 0.6305178305891925

../_images/02e038c0acf821aba919f8fd1f69f3469defb84b48958f3c4937c9c6613bddef.png
k = 10000
c, _ = mdav(X, len(X) // 2)
c0, _ = mdav(c[0], len(c[0]) // 2)
c1, _ = mdav(c[1], len(c[1]) // 2)
c00, cen00 = mdav(c0[0], k)
c01, cen01 = mdav(c0[1], k)
c10, cen10 = mdav(c1[0], k)
c11, cen11 = mdav(c1[1], k)

clusters = np.vstack((c00,c01,c10,c11))
centroids = np.vstack((cen00,cen01,cen10,cen11))

print_stats(clusters, centroids)
plot_results(clusters)
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---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In[8], line 10
      7 c10, cen10 = mdav(c1[0], k)
      8 c11, cen11 = mdav(c1[1], k)
---> 10 clusters = np.vstack((c00,c01,c10,c11))
     11 centroids = np.vstack((cen00,cen01,cen10,cen11))
     13 print_stats(clusters, centroids)

File ~\AppData\Local\Programs\Python\Python311\Lib\site-packages\numpy\core\shape_base.py:286, in vstack(tup, dtype, casting)
    219 @array_function_dispatch(_vhstack_dispatcher)
    220 def vstack(tup, *, dtype=None, casting="same_kind"):
    221     """
    222     Stack arrays in sequence vertically (row wise).
    223 
   (...)    284 
    285     """
--> 286     arrs = atleast_2d(*tup)
    287     if not isinstance(arrs, list):
    288         arrs = [arrs]

File ~\AppData\Local\Programs\Python\Python311\Lib\site-packages\numpy\core\shape_base.py:121, in atleast_2d(*arys)
    119 res = []
    120 for ary in arys:
--> 121     ary = asanyarray(ary)
    122     if ary.ndim == 0:
    123         result = ary.reshape(1, 1)

ValueError: setting an array element with a sequence. The requested array has an inhomogeneous shape after 1 dimensions. The detected shape was (2,) + inhomogeneous part.
k = 5
c, _ = mdav(X, len(X) // 2)
c0, _ = mdav(c[0], len(c[0]) // 2)
c1, _ = mdav(c[1], len(c[1]) // 2)
c00, _ = mdav(c0[0], len(c0[0]) // 2)
c01, _ = mdav(c0[1], len(c0[1]) // 2)
c10, _ = mdav(c1[0], len(c1[0]) // 2)
c11, _ = mdav(c1[1], len(c1[1]) // 2)

c000, cen000 = mdav(c00[0], k)
c001, cen001 = mdav(c00[1], k)
c010, cen010 = mdav(c01[0], k)
c011, cen011 = mdav(c01[1], k)
c100, cen100 = mdav(c10[0], k)
c101, cen101 = mdav(c10[1], k)
c110, cen110 = mdav(c11[0], k)
c111, cen111 = mdav(c11[1], k)

clusters = np.vstack(
    (
        c000,
        c001,
        c010,
        c011,
        c100,
        c101,
        c110,
        c111
    )
)

centroids = np.vstack(
    (
        cen000,
        cen001,
        cen010,
        cen011,
        cen100,
        cen101,
        cen110,
        cen111
    )
)

print_stats(clusters, centroids)
#plot_results(clusters)